A local gift shop sold bags of candy and cookies for Halloween. Bags of candy cost $$6.50$, and bags of cookies cost $$4.50$, and sales equaled $$35.50$ in total. There were $3$ more bags of cookies than candy sold. Find the number of bags of candy and cookies sold by the gift shop.
Explanation: Let $x$ equal the number of bags of candy and $y$ equal the number of bags of cookies. The system of equations is then: ${6.5x+4.5y = 35.5}$ ${y = x+3}$ Since we already have solved for $y$ in terms of $x$ , we can use substitution to solve for $x$ and $y$ Substitute ${x+3}$ for $y$ in the first equation. ${6.5x + 4.5}{(x+3)}{= 35.5}$ Simplify and solve for $x$ $ 6.5x+4.5x + 13.5 = 35.5 $ $ 11x+13.5 = 35.5 $ $ 11x = 22 $ $ x = \dfrac{22}{11} $ ${x = 2}$ Now that you know ${x = 2}$ , plug it back into $ {y = x+3}$ to find $y$ ${y = }{(2)}{ + 3}$ ${y = 5}$ You can also plug ${x = 2}$ into $ {6.5x+4.5y = 35.5}$ and get the same answer for $y$ ${6.5}{(2)}{ + 4.5y = 35.5}$ ${y = 5}$ $2$ bags of candy and $5$ bags of cookies were sold.